Question
In which quadrant would 0 be if cos0 =sqrrt 3/2 and sin0 =0-1/2
Answers
GPT-4o mini
The cosine and sine values you provided for an angle \(\theta\) seem to be inconsistent based on typical trigonometric functions.
1. The cosine value you mentioned is \(\cos(\theta) = \frac{\sqrt{3}}{2}\) which is correct for standard angles in trigonometry (specifically, \(\theta = 30^\circ\) or \(150^\circ\) in the unit circle).
2. However, you mentioned that \(\sin(\theta) = -\frac{1}{2}\). The sine value of \(-\frac{1}{2}\) typically corresponds to angles of \(210^\circ\) (or \(\frac{7\pi}{6}\) radians) and \(330^\circ\) (or \(\frac{11\pi}{6}\) radians).
Since \(\cos(\theta) = \frac{\sqrt{3}}{2}\) is positive, we are looking at the first or fourth quadrants. However, the sine value you provided is negative, which indicates that we are in the fourth quadrant.
To summarize:
- \(\cos(\theta) = \frac{\sqrt{3}}{2}\) corresponds to angles in the first and fourth quadrants.
- \(\sin(\theta) = -\frac{1}{2}\) confirms that \(\theta\) is indeed in the fourth quadrant.
Thus, \(\theta\) would be in the **fourth quadrant**.
1. The cosine value you mentioned is \(\cos(\theta) = \frac{\sqrt{3}}{2}\) which is correct for standard angles in trigonometry (specifically, \(\theta = 30^\circ\) or \(150^\circ\) in the unit circle).
2. However, you mentioned that \(\sin(\theta) = -\frac{1}{2}\). The sine value of \(-\frac{1}{2}\) typically corresponds to angles of \(210^\circ\) (or \(\frac{7\pi}{6}\) radians) and \(330^\circ\) (or \(\frac{11\pi}{6}\) radians).
Since \(\cos(\theta) = \frac{\sqrt{3}}{2}\) is positive, we are looking at the first or fourth quadrants. However, the sine value you provided is negative, which indicates that we are in the fourth quadrant.
To summarize:
- \(\cos(\theta) = \frac{\sqrt{3}}{2}\) corresponds to angles in the first and fourth quadrants.
- \(\sin(\theta) = -\frac{1}{2}\) confirms that \(\theta\) is indeed in the fourth quadrant.
Thus, \(\theta\) would be in the **fourth quadrant**.